Please see at TOEFL Clifs suggestion book at page 131
In America, they are called it “Modals+Perfective”.
Like, teacher should have explained you more.
Your concern is, as Teacher is here third person singular number so that why it shouldn’t be “Has” instead of “Have”.
Grammarians have made this structure this ways that are- would/could/should/must/might/may with “have” no “has or had”, these are fixed, no change whether it is with he/we-all are past meaning, though sometime possibility of present meaning , like:
The cause of death could have been bacteria.